In the following image, the left half contains alternating black and white pixels and the right half is is the same except the black and white pixels are swapped. On a standard RGB display, the two halves look the same. However, on RGBW (assuming no DPI scaling or zooming is being used), the two halves are completely different colors and they also change if you move the image around.
This is a problem because a pixel in RGBW cannot display as much information as a standard RGB pixel.